What is a Euler Angle?

Three sets of independent angular parameters used to determine the position of a fixed-point rotating rigid body are composed of nutation angle , precession angle (ie, precession angle) , and rotation angle . They were named after Euler first proposed it.

The Euler angle is a set of three independent angular parameters used to uniquely determine the position of a fixed-point rotating rigid body. It consists of a nutation angle , a precession angle , and a rotation angle . There are many ways to get them, the following is a common one.

The Eulerian angles are used to determine the position of a fixed-point rotating rigid body.

Academic pictures related to "Eulerhorn"

Euler Angle Applied Research

Euler angles are widely used in the study of rigid bodies in classical mechanics and the study of angular momentum in quantum mechanics.

In the case of rigid bodies, the xyz coordinate system is the global coordinate system , and the XYZ coordinate system is the local coordinate system . The global coordinate system is immovable; the local coordinate system is embedded in the rigid body. For the calculation of kinetic energy, it is usually simpler to use a local coordinate system; because the inertia tensor does not change with time. If you diagonalize the inertia tensor (which has nine components, six of which are independent), you get a set of principal axes and a moment of inertia (only three components).

In quantum mechanics, a detailed description of the form of SO (3) is very important for accurate calculations, and almost all research uses Euler angles as a tool. In the early research of quantum mechanics, physicists and chemists still held extremely sharp opposition to the abstract group theory method (called Gruppenpest); the trust in Euler angles was necessary.

Hall's measure of Euler angles

The Hall measurement of Euler angles has a simple form, usually preceded by a normalization factor 2/8.

Euler pt.

The unit quaternion, also known as Euler's parameter , provides another way to express three-dimensional rotation. This is equivalent to the description of special unitary groups. The quaternion method is faster in most calculations, easier to understand conceptually, and can avoid some technical problems, such as gimbal lock. For these reasons, many high-speed 3D graphics programs use quaternions.